Solve for x -4|x+2|=x-8

Problem

−4*|x+2|=x−8

Solution

1. Isolate the absolute value expression by dividing both sides of the equation by −4

−4*|x+2|=x−8

|x+2|=(x−8)/(−4)

|x+2|=−1/4*x+2

2. Set up two separate equations based on the definition of absolute value, |u|=a⇒u=a or u=−a

x+2=−1/4*x+2

x+2=−(−1/4*x+2)

3. Solve the first equation for x

x+1/4*x=2−2

5/4*x=0

x=0

4. Solve the second equation for x

x+2=1/4*x−2

x−1/4*x=−2−2

3/4*x=−4

x=−16/3

5. Check for extraneous solutions by substituting the values back into the original equation.
   For x=0

−4*|0+2|=0−8

−4*(2)=−8

−8=−8

For x=−16/3

−4*|−16/3+2|=−16/3−8

−4*|−10/3|=−40/3

−4*(10/3)=−40/3

−40/3=−40/3

Final Answer

x=0,−16/3

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